Being resourceful

  • Cuboids
    problem

    Cuboids

    Age
    11 to 14
    Challenge level
    filled star filled star filled star

    Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

  • The Spider and the Fly
    problem

    The spider and the fly

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

  • Lots of Lollies
    problem

    Lots of lollies

    Age
    5 to 7
    Challenge level
    filled star filled star filled star

    Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

  • Share Bears
    problem

    Share bears

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

  • The Tall Tower
    problem

    The tall tower

    Age
    5 to 7
    Challenge level
    filled star filled star filled star

    As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

  • Ladybird Count
    problem

    Ladybird count

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

  • Cut Nets
    problem

    Cut nets

    Age
    7 to 11
    Challenge level
    filled star filled star empty star

    Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

  • problem

    Up and down staircases

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

  • Odd Squares
    problem

    Odd squares

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

  • Sponge Sections
    problem

    Sponge sections

    Age
    7 to 11
    Challenge level
    filled star filled star empty star

    You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.